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Asymptotic formulae for generalized Freud polynomials. (English) Zbl 1295.30014
Summary: We establish Mehler-Heine type formulae for orthonormal polynomials with respect to generalized Freud weights. Using this type of asymptotics, we can give estimates of the value at the origin of these polynomials and of all their derivatives as well as the asymptotic behavior of the corresponding zeros.

##### MSC:
 30C10 Polynomials and rational functions of one complex variable 30E15 Asymptotic representations in the complex plane 33C45 Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.)
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